Question

If the equation of a transverse common tangent drawn to the circles \[ x^2+y^2-2x-10y+1=0 \] and \[ x^2+y^2+8x+14y+1=0 \] is \[ 5x+by+c=0, \] then \(b+c=\)

• A. \(17\)
• B. \(7\)
• C. \(12\)
• D. \(24\)

Hint:

For a common tangent, the perpendicular distance from each centre to the tangent equals the corresponding radius. For a transverse common tangent, the centres lie on opposite sides of the tangent.

Answer 1

The Correct Option is C